Spectral Inequalities for the Schrödinger operator

In this paper we deal with the so-called "spectral inequalities", which yield a sharp quantification of the unique continuation for the spectral family associated with the Schrödinger operator in R^d H_{g,V} = -\Delta_g + V (x), where \Delta_g is the Laplace-Beltrami operator with respect to an analytic metric g, which is a perturbation of the Euclidean metric, and V (x) a real valued analytic potential vanishing at infinity.